Structure Preserving Inversion: An Efficient Approach to Conditioning Stochastic Reservoir Models to Dynamic Data
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We propose a two-stage approach to data integration that combines elements of geostatistics within the framework of inverse modeling. First, we incorporate static data using traditional stochastic imaging techniques that are robust and computationally efficient. Next, we condition the resulting model to dynamic data using a novel approach called structure-preserving inversion. Unlike traditional inverse methods, the proposed approach involves a gradient-based iterative minimization procedure that perturbs reservoir properties (for example, permeability) only at selected pilot locations to match the production history. The resulting changes in properties at the pilot locations are then transferred to other locations by kriging that preserves the initial structure. Typically only about 10-15% of the grid points are used as pilot locations resulting in orders of magnitude savings in computation time compared to simulated annealing. Selection of pilot locations can be based either on sensitivity studies of the initial model or a priori knowledge of the reservoir under study. Multiple realizations of reservoir models conditioned to static and dynamic data can be generated by starting with different initial realizations. The proposed approach has been applied to synthetic as well as field examples. The synthetic example is designed to address several key issues such as computational efficiency, selection of pilot locations, convergence of the algorithm, and updating techniques. The field example is from the North Robertson Unit, a low permeability carbonate reservoir in west Texas and includes multiple patterns consisting of 42 wells. Water-cut history from producing wells is used to characterize permeability distribution to demonstrate the feasibility of the proposed approach for large-scale field applications.
author list (cited authors)
Xue, G., & Datta-Gupta, A.